Jeff Trigg is an Illinois Libertarian and he has first hand experience dealing with punitive ballot access signature requirements. He calculates the numbers, and it ain't pretty.
Let me add to his comments by noting that gathering petition signatures is very expensive and time consuming. A popular and well-funded candidate can wind up using all his cash and volunteers' efforts just to get on the ballot, and have none left over for the actual campaign.

Don't think that isn't exactly how the career politicians intend the system to work.

Here in Colorado ballot access was liberalized for the 2000 election cycle. The Libertarians and other parties ran quite a few candidates, with some success. Some legislators have been trying to restrict ballot access ever since.